A continuation like [...] would allow me to gain the initiative on this side of the board
means
A continuation like [...] can allow me to gain the initiative on this side of the board
or is there a difference?

Does Modern in Modern Chess Planning moddify chess or Planning and why?

The adjective modern qualifies the noun planning. But to be sure we need the context. It is possible to construct a sentence where the noun chess is qualified. You have raised one of the most difficult aspects of modern English usage; words acting outside their normal usage. A small point is that it is usual to refer to an adjective qualifying a noun not modifying a noun. An adverb is usually referred to as modifying a verb.

In your example the words are used:-

modern : pure adjective
chess : noun used as adjective
planning : gerund used as noun

So the word modern qualifies the noun planning.

No doubt on this forum there will be those who argue chess planning is a compound two word noun and that gerunds don't exist as in previous postings.

No doubt on this forum there will be those who argue chess planning is a compound two word noun and that gerunds don't exist as in previous postings.

Modern Chess something is a well used construction. Modern Chess Openings being a case in point. Modern Openings in Chess would have the same meaning. Modern Planning in Chess would be an alternative to Modern Chess Planning.

The title of the book could be Modern Planning if you knew it would be always categorised as chess.